I need help if someone can show me the steps to these 2 problems.

Problem #1

Use the properties for radicals to simplify each of the following expressions. Assume that all variables represent positive real numbers.

radical and inside of the radical theres a fraction that reads
(12x^3)/(5)

Problem #2
Simplify by combining like terms.
radical 63 minus 2radical 28+5radical 7

On the first, remember that x cubed is x squared times x.

you have a principle that says

sqrt (a^n * a) = a^(n/2) sqrt a

so bring the x squared out as x.

I cant follow the second.

Here is a good way to print radicals:

to get the √ sign, hold down the ALT key while you press 251 on the number pad, then release the ALT key.

I interpret your second question this way:
√63-2√28+5√7

you can only add or subtract like radicals, so in these kind of question they most likely want you to change them all to the same kind of radical.
Look for the lowest radical, usually the others can be changed to that.

hint: isn't 63 = 9*7 and 28=4*7 ???

To simplify the first problem, which is (12x^3)/5 inside a radical, you can use the property of radicals that states √(a^n * b) = a^(n/2) √b. In this case, the variable inside the radical is (12x^3)/5, so you can rewrite it as (√5)(√(12x^3)).

Next, simplify the expression inside the radical. Recall that x^3 is equal to x^2 times x, so you can rewrite it as (√5)(√(12x^2 * x)).

The property of radicals allows you to separate the product inside the square root, so you can rewrite it as (√5)(√12x^2)(√x).

Now, simplify further. Since 5 and 12 are both perfect squares, you can simplify them as (√(5 * 4))(√3)(√(x^2))(√x).

The square root of 4 is 2, so you have (√20)(√3)(x)(√x).

Finally, simplify (√20)(√3) to get (√60), which can be further simplified as (√(4 * 15)). The square root of 4 is 2, so the expression becomes (2)(√15)(x)(√x).

Thus, the simplified expression is 2√15x√x.

For the second problem, you have the expression √63 - 2√28 + 5√7.

To simplify this expression, start by analyzing the numbers under the radicals. Notice that 63, 28, and 7 can all be factored into a perfect square multiplied by another number. For example, 63 = 9 * 7, 28 = 4 * 7, and 7 is already a perfect square.

Now, rewrite the expression using the factored forms: √(9 * 7) - 2√(4 * 7) + 5√7.

Next, simplify the perfect square terms: 3√7 - 2(2√7) + 5√7.

Combine like terms: 3√7 - 4√7 + 5√7.

Now, you can perform the addition and subtraction of like radicals: (3 - 4 + 5)√7.

Simplify the coefficients: 4√7.

Therefore, the simplified expression is 4√7.